Aims. We attempt to extend the relation between the strengths of the interstellar lines and the distances to early-type stars to
objects beyond 1 kiloparsec, with the line saturation taken
into account.

Methods. We measure the K and H equivalent widths, and compute column densities for 262 lines of sight
towards early-type stars with available Hipparcos parallaxes (π). The targets are located within a few hundred parsecs of the Galactic
plane, and span all the range of Galactic longitudes. We fit the – parallax relation with a function of the form
, using a maximum-likelihood approach to take account of errors in both variables. We use the
resultant formula to estimate distances to stars in OB associations and clusters, and compare them to those found in the literature, usually
estimated by spectrophotometric methods.

Results. For lines of sight with , we obtain the following approximate formula for the distance: , where the equivalent widths and are in mÅ, and the
distance in parsecs. The errors in , resulting from the uncertainty in the fit parameters
and errors in the equivalent widths, are typically about 15% of the distance. We can also expect the equation not to hold for objects
situated farther than a few hundred parsecs from the Galactic plane. We find several cases of significant column density differences between
association or cluster members, especially notable in the Trumpler 16 cluster, indicating either a local contribution to the
column density, or background/foreground stars being confused with members. The ratio appears
to depend on the Galactic longitude, being highest in the range 70° < l < 120° and lowest for 200° < l <
300°. This effect may be due to large-scale structure being present in the layer, or to the nonmember confusion being
enhanced in these directions.

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